№ 1. 14/27 + 2/27 = 16/27; 11/35 + 12/35 = 23/35; 17/60 + 12/60 = 29/60; 32/55 + 23/55 = 55/55 = 1; 5/33 + 6/33 = 11/33 = 1/3; 12/48 + 12/48 = 24/48 = 1/2; 8/99 + 91/99 = 99/99 = 1; 77/90 + 13/90 = 90/90 = 1
№ 2. 1/2 + 1/2 + 1/2 + 1/2 = 4/2 = 2; 1/3 + 2/3 + 1/3 + 5/3 = 9/3 = 3; 7/13 + 4/13 + 2/13 = 13/13 = 1; 1/96 + 5/96 + 11/96 + 31/96 = 48/96 = 1/2; 1/42 + 15/42 + 17/42 + 9/42 = 42/42 = 1; 19/78 + 53/78 + 37/78 + 21/78 = 130/78 = 1 52/78 = 1 2/3
№ 3. 1/2 +1/3 = 3/6 + 2/6 = 5/6; 1/2 + 1/5 = 5/10 + 2/10 = 7/10 = 0,7; 1/3 + 1/4 = 4/12 + 3/12 = 7/12; 1/4 + 1/5 = 5/20 + 4/20 = 9/20; 1/2 + 1/4 = 2/4 + 1/4 = 3/4; 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2; 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3; 1/4 + 1/8 = 2/8 + 1/8 = 3/8
№ 4. 1/10 + 7/100 = 10/100 + 7/100 = 17/100 = 0,17; 21/100 + 1/10 = 21/100 + 10/100 =31/100 = 0,31; 3/5 + 9/10 = 6/10 + 9/10 = 15/10 = 1 5/10 = 1,5
Пусть х тг - цена апельсинов; у тг - цена лимонов.
{7х + 4у = 7800
{5х - 2у = 1200
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Домножим второе уравнение системы на 2
{7х + 4у = 7800
{10х - 4у = 2400
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Сложим оба уравнения
17х + 0у = 10200
х = 10200 : 17
х = 600
Подставим значение х в любое уравнение системы
7 · 600 + 4у = 7800 или 5 · 600 - 2у = 1200
4200 + 4у = 7800 3000 - 2у = 1200
4у = 7800 - 4200 2у = 3000 - 1200
4у = 3600 2у = 1800
у = 3600 : 4 у = 1800 : 2
у = 900 у = 900
ответ: 600 тенге - цена апельсинов; 900 тенге - цена лимонов.